Question

While on a road trip, Steve drove 300 miles in 5 hours. After stopping for gas, he drove an additional 120 miles in 2 hours. Does this situation
represent a direct variation? If so, what are the independent and dependent variables?

Answer 1

Answer:

The given situation is in direct variation.

The dependent variable is the distance covered and the independent variable is the number of hours.                

Step-by-step explanation:

We are given the following information in the question:

Steve drove 300 miles in 5 hours.

After stopping for gas, he drove an additional 120 miles in 2 hours.

We calculate the ratios and if these ratios are equal then, we can say that the situation represent a direct variation.

For direct variation, the equation is of the form y = kx that is , we can write,

$\displaystyle\frac{y}{x} = k$

To check the ratio:

$\displaystyle\frac{300}{5} = \frac{300+120}{5+2} =\frac{420}{7} = 60$

Thus, the given situation is in direct variation.

The dependent variable is the distance covered and the independent variable is the number of hours.